Polygon Lattice Points

Given a polygon, your task is to calculate the number of lattice points inside the polygon and on its boundary. A lattice point is a point whose coordinates are integers. The polygon consists of n vertices (x_1,y_1),(x_2,y_2),\dots,(x_n,y_n). The vertices (x_i,y_i) and (x_{i+1},y_{i+1}) are adjacent for i=1,2,\dots,n-1, and the vertices (x_1,y_1) and (x_n,y_n) are also adjacent.

Input

The first input line has an integer n: the number of vertices. After this, there are n lines that describe the vertices. The ith such line has two integers x_i and y_i. You may assume that the polygon is simple, i.e., it does not intersect itself.

Output

Print two integers: the number of lattice points inside the polygon and on its boundary.

Constraints

$3 \le n \le 10^5$

$-10^9 \le x_i, y_i \le 10^9$

Example

Input

4
1 1
5 3
3 5
1 4

Output

6 8